Diameter Of Particle Given Settling Velocity With Respect To Specific Gravity Calculator

Formula Used:

\[ D = \frac{3 \times C_D \times V_s^2}{4 \times g \times (G - 1)} \]

Drag Coefficient (C_D):

(dimensionless)

Settling Velocity (V_s):

m/s

Specific Gravity of Particle (G):

(dimensionless)

Diameter (D):

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1. What is the Diameter Calculation Formula?

The formula calculates the diameter of a particle based on its settling velocity, drag coefficient, and specific gravity relative to the fluid. This is particularly useful in fluid mechanics and sedimentation processes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D = \frac{3 \times C_D \times V_s^2}{4 \times g \times (G - 1)} \]

Where:

\( D \) — Diameter of the particle (m)
\( C_D \) — Drag coefficient (dimensionless)
\( V_s \) — Settling velocity (m/s)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( G \) — Specific gravity of particle (dimensionless)

Explanation: The formula relates the particle diameter to its terminal settling velocity, accounting for fluid resistance through the drag coefficient and the buoyancy effect through specific gravity.

3. Importance of Particle Diameter Calculation

Details: Accurate particle diameter calculation is essential in various engineering applications including sedimentation tanks design, filtration systems, air pollution control, and mineral processing operations.

4. Using the Calculator

Tips: Enter drag coefficient (positive value), settling velocity in m/s (positive value), and specific gravity (must be greater than 1). All values must be valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for drag coefficient?
A: Drag coefficient varies with particle shape and Reynolds number, typically ranging from 0.1 to 2.0 for spherical particles in different flow regimes.

Q2: How does specific gravity affect the diameter calculation?
A: Higher specific gravity (denser particles) results in smaller calculated diameter for the same settling velocity, as denser particles settle faster.

Q3: When is this formula most accurate?
A: The formula is most accurate for spherical particles in laminar flow conditions (low Reynolds numbers).

Q4: What are the limitations of this calculation?
A: The calculation assumes spherical particles, constant drag coefficient, and may not account for particle interactions or non-Newtonian fluid behavior.

Q5: Can this be used for irregularly shaped particles?
A: For irregular particles, equivalent spherical diameter can be calculated, but results should be interpreted with caution as shape affects both drag coefficient and settling behavior.